{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XEEXXYPL6UXVHGVYJWRTDJGKFQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d54d538c99c18c0f0de78ab267aff062cf4663b5603d54df26b09354df87328a","cross_cats_sorted":["cs.DM","cs.DS","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-25T16:36:08Z","title_canon_sha256":"9290d9000e8150d6da6adb9dca26db02a67d49691ed5a819489c4426dfa75560"},"schema_version":"1.0","source":{"id":"2507.19417","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.19417","created_at":"2026-07-05T11:57:58Z"},{"alias_kind":"arxiv_version","alias_value":"2507.19417v2","created_at":"2026-07-05T11:57:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19417","created_at":"2026-07-05T11:57:58Z"},{"alias_kind":"pith_short_12","alias_value":"XEEXXYPL6UXV","created_at":"2026-07-05T11:57:58Z"},{"alias_kind":"pith_short_16","alias_value":"XEEXXYPL6UXVHGVY","created_at":"2026-07-05T11:57:58Z"},{"alias_kind":"pith_short_8","alias_value":"XEEXXYPL","created_at":"2026-07-05T11:57:58Z"}],"graph_snapshots":[{"event_id":"sha256:cee2de9bab5ef463a62d7b3a334b6eecfc656ff521615ad2548cfc2c450b6129","target":"graph","created_at":"2026-07-05T11:57:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.19417/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is a classical result that a random permutation of $n$ elements has, on average, about $\\log n$ cycles. We generalise this fact to all directed $d$-regular graphs on $n$ vertices by showing that, on average, a random cycle-factor of such a graph has $\\mathcal{O}((n\\log d)/d)$ cycles. This is tight up to the constant factor and improves the best previous bound of the form $\\mathcal{O}(n/\\sqrt{\\log d})$ due to Vishnoi. Our results also yield randomised polynomial-time algorithms for finding such a cycle-factor and for finding a tour of length $(1+\\mathcal{O}((\\log d)/d)) \\cdot n$ if the graph","authors_text":"Alp M\\\"uyesser, Ant\\'onio Gir\\~ao, Eoin Hurley, Lukas Michel, Micha Christoph, Nemanja Dragani\\'c","cross_cats":["cs.DM","cs.DS","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-25T16:36:08Z","title":"Cycle-factors of regular graphs via entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19417","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ebbc6929d2ae6d3e5d5b1872b255e6dfb963422076d1471932ab3433c0b5a9f1","target":"record","created_at":"2026-07-05T11:57:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d54d538c99c18c0f0de78ab267aff062cf4663b5603d54df26b09354df87328a","cross_cats_sorted":["cs.DM","cs.DS","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-25T16:36:08Z","title_canon_sha256":"9290d9000e8150d6da6adb9dca26db02a67d49691ed5a819489c4426dfa75560"},"schema_version":"1.0","source":{"id":"2507.19417","kind":"arxiv","version":2}},"canonical_sha256":"b9097be1ebf52f539ab84da331a4ca2c0b2117f541fc40a0d759792c429c8f08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9097be1ebf52f539ab84da331a4ca2c0b2117f541fc40a0d759792c429c8f08","first_computed_at":"2026-07-05T11:57:58.233900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:57:58.233900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nK4Z4XVUcJQZyrIGTgOLn+PjYjqwnOg7EkqkzlEsaVYAFBdauSc/T2UeLSmpRv0ouAVd0U8hWEN4FI2kDjk/Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:57:58.234496Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.19417","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebbc6929d2ae6d3e5d5b1872b255e6dfb963422076d1471932ab3433c0b5a9f1","sha256:cee2de9bab5ef463a62d7b3a334b6eecfc656ff521615ad2548cfc2c450b6129"],"state_sha256":"d473ae2ec42eebdffe212df1a25701d9c4e889e56f11fae8380298098422c924"}